e/a classification of Hume–Rothery Rhombic Triacontahedron-type approximants based on all-electron density functional theory calculations

Mizutani, U; Inukai, M; Sato, H; Zijlstra, E S; Lin, Q

doi:10.1080/14786435.2014.913820

Title: e/a classification of Hume–Rothery Rhombic Triacontahedron-type approximants based on all-electron density functional theory calculations

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Abstract

There are three key electronic parameters in elucidating the physics behind the Hume–Rothery electron concentration rule: the square of the Fermi diameter (2kF)2, the square of the critical reciprocal lattice vector and the electron concentration parameter or the number of itinerant electrons per atom e/a. We have reliably determined these three parameters for 10 Rhombic Triacontahedron-type 2/1–2/1–2/1 (N = 680) and 1/1–1/1–1/1 (N = 160–162) approximants by making full use of the full-potential linearized augmented plane wave-Fourier band calculations based on all-electron density-functional theory. We revealed that the 2/1–2/1–2/1 approximants Al13Mg27Zn45 and Na27Au27Ga31 belong to two different sub-groups classified in terms of equal to 126 and 109 and could explain why they take different e/a values of 2.13 and 1.76, respectively. Among eight 1/1–1/1–1/1 approximants Al3Mg4Zn3, Al9Mg8Ag3, Al21Li13Cu6, Ga21Li13Cu6, Na26Au24Ga30, Na26Au37Ge18, Na26Au37Sn18 and Na26Cd40Pb6, the first two, the second two and the last four compounds were classified into three sub-groups with = 50, 46 and 42; and were claimed to obey the e/a = 2.30, 2.10–2.15 and 1.70–1.80 rules, respectively.

Authors:: Mizutani, U; Inukai, M; Sato, H; Zijlstra, E S; Lin, Q

Publication Date:: Fri May 16 00:00:00 EDT 2014

Research Org.:: Ames Lab., Ames, IA (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1157652

Report Number(s):: IS-J 8367
Journal ID: ISSN 1478-6435

DOE Contract Number:: DE-AC02-07CH11358

Resource Type:: Journal Article

Journal Name:: Philosophical Magazine (2003, Print)

Additional Journal Information:: Journal Volume: 94; Journal Issue: 22; Journal ID: ISSN 1478-6435

Publisher:: Taylor & Francis

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE; Hume-Rothery electron concentration rule, FLAPW-Fourier method, 2/1-2/1-2/1 approximants, RT-type approximants, interference condition, Hume-Rothery stabilization mechanism

Citation Formats


                    Mizutani, U, Inukai, M, Sato, H, Zijlstra, E S, and Lin, Q. e/a classification of Hume–Rothery Rhombic Triacontahedron-type approximants based on all-electron density functional theory calculations.  United States: N. p., 2014. 
        Web.  doi:10.1080/14786435.2014.913820.

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                    Mizutani, U, Inukai, M, Sato, H, Zijlstra, E S, & Lin, Q. e/a classification of Hume–Rothery Rhombic Triacontahedron-type approximants based on all-electron density functional theory calculations.  United States.  https://doi.org/10.1080/14786435.2014.913820

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                    Mizutani, U, Inukai, M, Sato, H, Zijlstra, E S, and Lin, Q. 2014.  
        "e/a classification of Hume–Rothery Rhombic Triacontahedron-type approximants based on all-electron density functional theory calculations".  United States.  https://doi.org/10.1080/14786435.2014.913820.

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@article{osti_1157652,

  title        = {e/a classification of Hume–Rothery Rhombic Triacontahedron-type approximants based on all-electron density functional theory calculations},

  author       = {Mizutani, U and Inukai, M and Sato, H and Zijlstra, E S and Lin, Q},

  abstractNote = {There are three key electronic parameters in elucidating the physics behind the Hume–Rothery electron concentration rule: the square of the Fermi diameter (2kF)2, the square of the critical reciprocal lattice vector and the electron concentration parameter or the number of itinerant electrons per atom e/a. We have reliably determined these three parameters for 10 Rhombic Triacontahedron-type 2/1–2/1–2/1 (N = 680) and 1/1–1/1–1/1 (N = 160–162) approximants by making full use of the full-potential linearized augmented plane wave-Fourier band calculations based on all-electron density-functional theory. We revealed that the 2/1–2/1–2/1 approximants Al13Mg27Zn45 and Na27Au27Ga31 belong to two different sub-groups classified in terms of equal to 126 and 109 and could explain why they take different e/a values of 2.13 and 1.76, respectively. Among eight 1/1–1/1–1/1 approximants Al3Mg4Zn3, Al9Mg8Ag3, Al21Li13Cu6, Ga21Li13Cu6, Na26Au24Ga30, Na26Au37Ge18, Na26Au37Sn18 and Na26Cd40Pb6, the first two, the second two and the last four compounds were classified into three sub-groups with = 50, 46 and 42; and were claimed to obey the e/a = 2.30, 2.10–2.15 and 1.70–1.80 rules, respectively.},

  doi          = {10.1080/14786435.2014.913820},

  url          = {https://www.osti.gov/biblio/1157652},
  journal      = {Philosophical Magazine (2003, Print)},

  issn         = {1478-6435},

  number       = 22,

  volume       = 94,

  place        = {United States},

  year         = {Fri May 16 00:00:00 EDT 2014},

  month        = {Fri May 16 00:00:00 EDT 2014}

}

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